The paper presents a rather general formulation of a porous medium deformation coupled with a fluid flowing through the pores within the framework of physical and geometric nonlinearity. The boundary-value problem is formulated in terms of the solid phase displacement increment, fluid pressure and porosity increments in the form of differential and variational equations. The equations were derived from the general conservation laws of Continuum Mechanics using spatial averaging over a representative volume element (RVE). The model takes into account the porosity and permeability evolutions during deformation process. The equations of filtration and porosity evolution are formulated in the material coordinate system related to the solid phase, according to the idea of Arbitrary Lagrangian–Eulerian (ALE) approach. The linearization of variational equations was done using Gateaux differentiation technique. The proper finite elements were used for the spatial discretization of the saddle system of equations to satisfy well-known Ladyzhenskaya–Babuška–Brezzi (LBB) correctness condition. A generalization of the implicit time integration scheme with internal iterations at each time step according to the Uzawa method is employed. The convergence of the iterative process is partly theoretically studied. The formulation is numerically implemented in the form of a self-made computer code. Examples of calculations are given.

本文在物理和几何非线性的框架内提出了多孔介质变形与流过孔隙的流体相结合的相当一般的公式。边值问题用微分和变分方程形式的固相位移增量、流体压力和孔隙度增量来表述。这些方程是从连续介质力学的一般守恒定律推导出来的，它使用代表性体积元素 (RVE) 上的空间平均。该模型考虑了变形过程中孔隙度和渗透率的演变。根据任意拉格朗日-欧拉（ALE）方法的思想，在与固相相关的材料坐标系中制定了过滤和孔隙度演化方程。变分方程的线性化是使用 Gateaux 微分技术完成的。适当的有限元用于马鞍方程组的空间离散化以满足众所周知的 Ladyzhenskaya-Babuška-Brezzi (LBB) 正确性条件。采用根据 Uzawa 方法在每个时间步进行内部迭代的隐式时间积分方案的推广。对迭代过程的收敛性进行了部分理论研究。该公式以自制计算机代码的形式在数字上实现。给出了计算示例。采用根据 Uzawa 方法在每个时间步进行内部迭代的隐式时间积分方案的推广。对迭代过程的收敛性进行了部分理论研究。该公式以自制计算机代码的形式在数字上实现。给出了计算示例。采用根据 Uzawa 方法在每个时间步进行内部迭代的隐式时间积分方案的推广。对迭代过程的收敛性进行了部分理论研究。该公式以自制计算机代码的形式在数字上实现。给出了计算示例。